# pol1v.py

class pol1v (list):
  def __add__ (A,B):
    if not isinstance(B,pol1v): return A+pol1v(A.tipo,B)
    if not A.lun: return B
    if not B.lun: return A
    lunA=A.lun; lunB=B.lun; coeff=[]
    if lunA<=lunB:
      for i in xrange(lunA): coeff.append(A[i]+B[i])
      for i in xrange(lunA,lunB): coeff.append(B[i])
      return pol1v(A.tipo,*coeff)
    else: return B+A
  def __call__ (A,alfa):
    b=0
    for ak in reversed(A): b=b*alfa+ak
    return b
  def __init__ (A,tipo,*coeff):
    A.extend(map(tipo,coeff)); A.riduci()
    A.tipo=tipo; A.lun=len(A)
  def __mul__ (A,B):
    if not isinstance(B,pol1v): return A*pol1v(A.tipo,B)
    if not A.lun or not B.lun: return pol1v(A.tipo,0)
    if A.lun==1: a0=A[0]; return pol1v(A.tipo,*map(lambda x: a0*x,B))
    if B.lun==1: b0=B[0]; return pol1v(A.tipo,*map(lambda x: b0*x,A))
    coeff=[]
    for k in xrange(A.lun+B.lun-1):
      ck=0
      for i in xrange(A.lun):
        if 0<=k-i<=B.lun-1: ck+=A[i]*B[k-i]
      coeff.append(ck)
    return pol1v(A.tipo,*coeff)
  def __neg__ (A): return pol1v(A.tipo,*map(lambda x: -x,A))
  def __radd__ (A,B):
    if not isinstance(B,pol1v): return A+B
  def __rmul__ (A,B):
    if not isinstance(B,pol1v): return A*B
  def __rsub__ (A,B):
    if not isinstance(B,pol1v): return -A+B
  def __str__ (A):
    if A.tipo==complex: return str(list(A))
    if not A.lun: return '0'
    u=[]; potx=''
    for i,a in enumerate(A):
      if not a: potx+='x'; continue
      if a==1 and i>0: b=' + '
      elif a==-1 and i>0: b=' - '
      elif a>0: b=' + %s' %(str(a))
      else: b=' - %s' %(str(-a))
      u.append('%s%s' %(b,potx)); potx+='x'
    u=''.join(u).lstrip()
    if u.startswith('+'): u=u[1:].lstrip()
    return u
  def __sub__ (A,B): return A+(-B)
  def der (A):
    if A.lun<=1: return pol1v(A.tipo,0)
    u=[]
    for i,a in enumerate(A[1:]): u.append((i+1)*a)
    return pol1v(A.tipo,*u)
  def riduci (A):
    while A and not A[-1]: A.pop()
  def sviluppo (A,alfa):
    coeff=[]; g=A; fatt=1.0
    for k in xrange(A.lun+1):
      coeff.append(g(alfa)/fatt); g=g.der(); fatt*=(k+1)
    return pol1v(A.tipo,*coeff)